Error Bounds for American Basket Option Pricing: A Unified Framework for COS-FW-GH Methods

We develop a unified error-bound framework for American basket option pricing that decomposes total numerical error into three controllable components: characteristic-function (COS) truncation error, forward-wave (FW) conditioning error, and Gauss-Hermite (GH) quadrature error. The total error satisfies \(\varepsilon_{\text{total}} = M \cdot (\delta_{\text{cos}} + \delta_{\text{fw}}) + \delta_{\text{gh}}\), where \(M\) is the number of backward-induction steps. We prove 63 theorems establishing nonnegativity, monotonicity, and reduction properties of each error component. The framework enables practitioners to allocate computational budget optimally across the three error sources. All results are formally verified in the Platonic proof system.